But you asked box so I am thinking you want to know if the main breaker determines the size of the box?

Sizing a breaker box is both science and experience, understanding the TYPES and AMOUNTS of particular loads, it is not a matter of 10 15amp breakers is a 150 amp box

Below this link has two options for connecting links, both will answer everything you asked plus why this is a very good one please see both links right to the right of the first page, with two arrows,

Notice they say estimate, there is a reason for that, on the first arrow, then on the second it tells you how to identify and even acquire parts for many brands and types of boxes,

The bottom line is breakers protect wire not devices, but it is step by step process first you find the size of the device and amount of power it will use, inductive loads such as motor heavy loads like a refrigerator, have a heavy inrush load sometimes 10 times the full load rating you will see some are rated in va volt amps,

The idea is to decide on the total worse case use, then individual wire sizes, then breakers to protect that wire size AND LENGTH and TYPE OF WIRE<

But remember breakers are not good for protecting devices, they react too slow, many high value devices have internal FUSES to protect the device, if a device is critical and does not have fuses then a separate fuse block is the protection you need,

For example if there is an outside condensing unit for an air conditioner, you will often see a fused disconnect on the outside, it allows for servicing the unit safely and for fused protection when in operation,

Now days with so many electronics and USB chargers they predict we will see two kinds of services in homes one for the low voltage chargers for pods and pads, and phones and then the normal service,

With surges being a huge problem for sensitive electronics, you really need two things, one is a whole house surge protector and then an individual protector for the device itself,

Good protectors for individual devices are UPS units that isolate the sensitve electronics from both externally created surges, and the individual protection as more protection from those surges and ALSO from internally produced surges,

It is very complex in this day and age of many devices not only having a large motor load but also controlled by modern electronics.

Just remember it is not a simple add it up type of calculation it involves types of load, size of the area [why would you need the size of the area of the house? they ESTIMATE the amount of central heating and cooling and the amount of power it would take to do the job, along with amount of lighting ESTIMATED so on ]

So you have types of loads, size of area, hard wired devices right to a breaker, then devices that are plugged into an outlet, there is a lot to it, plus the contractor will know not only the NEC codes for the particular location, but also the local codes that might be modified for a particular location for example I live in a large city that uses one version of the NEC within a mile is a smaller city which uses a different version of the NEC, you might want to look at the NEC website it will make your eyes glaze over but you will get an idea of the different conventions and regulations that vary all over, but the two links above the first a calculating tool, and the second with two sub links one that sizes also and the second that IDENTIFIES

AGE the second link also has older fused mains, and explains the sizing, but you will find statements like this

Identify 100-Amp Circuit Breaker Panels:

Based only on apparent panel size and provision for 24 circuits, this larger panel at left, showing a modern main CB at the top and two 12-breaker columns is at least a 100 Amp box, maybe 150 Amps.

So that right there tells you the main breaker is not representive of the box but a range Quick story and warning, if you are converting or installing get references and don't DON'T just have an estimator come to your home, before they come to your home, YOU go to their shop or office, and take a tour, there are too many fancy websites that in no way represent what is really there, the shiny sharp website might be a metal garage in some backyard, so make sure you get references and you visit their facilities before they come to you. Your questions are very good, but very wide open, so there is a lot to read, but good for you for getting an education before you begin any electrical project

Installing a main box and breakers should always be done by a licensed and known electrical contractor, there are so many considerations it is not a DIY project, but the the links will answer your questions

About Electrical Wiring in the Home
This site answers questions related to home electrical wiring, home wiring, general electrical help,and other electrical questions related to aleternating current (AC). You can find help on the National Electical Code, home electrical issues, wiring electrical outlets, installing lighting, electrical grounding, and general electrical help for do-it-yourself projects not require an electrician. If you do not see your home electrical wiring question answered in this area then please ask your electrical wiring question here

Will Babbitt

Expertise

Electrical issues of all types, wiring, control, appliances, components, specialty in Electric MOTOR or APPARATUS trouble shooting, electric motors, electrical problems, single phase, three phase, DC, capacitors, elevator MG-Sets, modifications, reverse engineering, VFD Drives, single to three phase convertors.
Repair of most any electrical/mechanical/electronic apparatus, OEM, AC, DC, Industrial Applications,
Three phase, single phase failure mode, determining the root cause of the equipment failure BEFORE failure repeats,
Antique appliances, electric motors, fans, ceiling fans, base mount fans, poor equipment performance,
Modifications, habitual failures, vibration, redesign, obsolete issues, collectible items restored, rewinding. Owner of EMR Repair Inc www.emrrepair.com
More information on electric motors, under Engineering/Motors
Ask about any electrical or mechanical problems in the home, office, or even at your work.
B2B or business to business CONSULTING I can do but it would be a much more complex issue, that would require a significant amount of time.
repair@mearservice.com from there we can discuss and begin work on about anything.
Industrial electric motors, controls, troubleshooting, vibration, alignment, any type of industrial or commercial electric/electrcical equipment
For the home owner, renter, apartment if you have odd things going on, describe to me, photos are normally very helpful, appliances, heating and air conditioning issues, light switches, installation, DIY PROJECTS FOR THOSE NOT EDUCATED IN ELECTRICAL, we can do some things, but for safety and sanity reasons, I may refer you to a local electrician, and help you find one, help you with pricing and even speak directly with anyone you hire if you have issues,

Experience

Over thirty years with a major repair and sales company, VP of Operations, and former owner of my own specialty repair shops,
MEAR Services local to Kansas City Missouri
EMR Repair Inc., located in Kansas City Missouri,
2014 sold both businesses to JCI Industries, Lee's Summit Missouri wbabbitt@jciind.com
Evaluation and repair of electrical/mechanical apparatus. Electrical and mechanical repairs, trouble shooting including, vibration and balance issues.
About.com provides this service, and the huge costs to provide help on about any subject. They provide the servers, the people to vet the experts, costs that would be the same as operating a good sized business,
They should be appreciated for what they do, the huge costs and the great help they provide for free,
Electric motor questions, can be answered here but there is a dedicated category that has other experts to help and add to a solution.
Other common questions, are noises in the walls, breakers tripping, devices not starting or shutting down for no apparent reason, smoke alarms buzzing, thermostat change outs, or sizing wire or needing information for a new project, but anything can be resolved, anything, with enough effort and patience,
DIY, with electrical is possible, but in most cases the use of a simple ohm meter or volt meter is needed, they can be purchased at any hardware store for a few bucks.
If you have smoke, or smell smoke, don't be writing me, call 911 the Fire Department has no problem looking for smoke smells, better then spraying water on a blazing fire.
DO NOT GET CAUGHT INVESTIGATING AND TRAPPED IN A BASEMENT LOOKING FOR A BLOWER FAILING<
As to the tip jar, it is up to you, it is appreciated, every expert spends out of pocket that I know, we spend on IP time, computer wear, printing documents, books, and of course our time, but if we prevent a $400 service call, we did well,

OrganizationsFormer IBEW, EASA, IEEE, UL, ..............

PublicationsSEE ELECTRIC MOTOR CATEGORY

Education/Credentials10 plus years, various Technical Schools, followed by Industrial College Credit and non Credit Courses, electronics courses, experience in most any electrical apparatus, electric motors and generators, AC OR DC, fractional to above 5000HP, other electrical apparatus, slip rings, sleeve [plain] bearings, lubrication, identification-no data plate, control components, service and sales.
I have continued night schools for decades, the list is extensive.
I have been in the business of repairing most anything with wires or mechanical parts for decades, I have some helpful hints and directions you won't have to dig up. Or hopefully not have to pay a huge service call invoice to find.